2025 DSS PRELIMS P2 Q4

2025 DSS PRELIMS P2 Q4

Secondary 4

8 marks

Show that \(\dfrac{d}{dx}(\cot x)=-\cosec^2 x\).[4]
Hence find the value of \(\displaystyle \int_{\frac{\pi}{4}}^{\frac{\pi}{3}} -\cot^2 x\, dx\).[4]

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Answer:(a) \(\dfrac{d}{dx}(\cot x)=-\cosec^2x\) (b) \(\dfrac{\pi}{12}+\dfrac{1}{\sqrt3}-1\approx-0.161\)

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